Maximizing the amount of signal power delivered by an RF transmitter to an antenna is an important goal of every wireless system. This power maximization is achieved by matching the antenna input impedance to the output impedance of a transmitter. A conventional antenna transmitter system 100, shown in FIG. 1, comprises a passive matching network 101 inserted between a transmitter 102 and an antenna 103. The passive matching network 101 receives a signal solely from the transmitter 102 and delivers power to the antenna 103, while it is not connected to any external energy source. The passive network 101 typically comprises one or more capacitors and one or more inductors, or one or more segments of a transmission line, which can be arranged in several configurations generally known in the art of impedance matching. The purpose of the passive network 101 is to transform the impedance of antenna 103 (ZA=RA+jXA, where RA and XA are the antenna input resistance and the antenna input reactance, respectively) into a system impedance Z0 (usually 50 ohms). The transformation is needed for an efficient transfer of the energy from the transmitter 102 to the antenna 103. It is well known that, for every passive matching network, a matching bandwidth with maximal allowable modulus of a reflection coefficient is constrained by Bode-Fano criterion. A bandwidth constraint is a direct consequence of an inherent fundamental dispersion property of all reactive networks (the networks that comprise only capacitors or only inductors or only transmission lines, or any arbitrary combination of these elements). The fundamental dispersion constraint is given by Foster reactance theorem:
                    ∂                  [                      X            ⁡                          (              ω              )                                ]                            ∂        ω              >    0    ,                    ∂                  [                      B            ⁡                          (              ω              )                                ]                            ∂        ω              >    0.  Here, X and B are a reactance and a susceptance, respectively while ω represents the angular frequency. Due to Foster theorem, every passive matching network inevitably operates within a finite bandwidth. The background information on Foster reactance theorem and passive matching is available in publicly available textbooks, such as, D. M. Pozar, “Microwave Engineering”, Willey 1998.
Modern wireless communication systems use high data rates with wide channel bandwidths. In addition, many portable communication devices (cell phones, smart phones, laptops, military mobile transceivers) as well as some fixed communication systems (broadcasting short-wave transmitters) use antennas of a very small size (in terms of a wavelength). It is well known that an impedance of a small antenna is inevitably highly reactive, which significantly limits the achievable matching bandwidth (for instance, see W. L. Stutzman, G. A. Thiele, “Antenna Theory and Design”, Willey 2012). Quite often, a passive matching network cannot achieve an acceptable impedance match within a full desired bandwidth. The typical fractional bandwidth, defined as useful bandwidth divided by its center frequency, achievable using a passive matching of a small antenna ranges between 10 to 15%. On the other hand, Non-Foster Networks can be used to realize significantly wider matching bandwidths. Non-Foster Networks are active networks, namely, they include an energy source, and contain so-called Non-Foster elements: “negative” capacitors and “negative” inductors. These active components are referred to as Non-Foster elements because they do not obey Foster reactance theorem mentioned above. In brief, active broadband matching relies on a compensation of a frequency dispersion of ordinary reactive network with the ‘inverse’ dispersion provided by a ‘negative’ non-Foster network. This active compensation yields (theoretically) infinite bandwidth as is well known in the art. See publicly available documents, such as: S. E. Sussman-Fort, R. M. Rudish, “Non-Foster impedance matching of electrically-small Antennas,” IEEE Transactions on Antennas and Propagation, pp. 2230-2241, vol 57, August 2009, S. Koulouridis, “Impedance matching for small antennas using passive and active circuits”, John Volakis, Chi-Chih Chen, Kyohei Fujimoto, Eds., “Small Antennas: Miniaturization Techniques & Applications”, New York: McGraw Hill, 2010, pp. 361-388). In practice, the ‘negative’ elements are realized using appropriate electronic circuitry that are generally referred to as “negative impedance converters” (NICs). A number of different NIC designs has been studied in the prior art (see, for example, J. G. Linvill, “Transistor Negative Impedance Converters” Proceedings IRE, Vol. 41, pp. 725-729, June 1953; Stephen E. Sussman-Fort, “Gyrator-Based Biquad Filters and Negative Impedance Converters for MicroWaves,” International Journal of RF and Microwave Computer-Aided Engineering, Vol. 8, No. 2, pp. 86-101, 1998; D. Segovia-Vargas, V. Gonzalez-Posadas, J. L. Jimenez, E. Ugarte-Munoz, J. Herraiz-Martinez and L. E. Garcia-Munoz, “Negative Impedance Converters (NICs) in the Design of Small and Multifrequency Antennas”, Proceedings of the 5th European Conference on Antennas and Propagation (EUCAP), 2011, p. 2724-272).
FIG. 2 illustrates an example of a conventional actively matched transmitter system 200 comprising of a signal source 202, passive resistance matching network 205, the NIC 201 and an antenna 203. The NIC 201 is attached to a load 204. The signal is generated at the signal source 202 and transmitted to the antenna 203 via the passive matching network 205 and NIC 201. In order to cancel the reactance of the antenna 203, the NIC load impedance 204 has to be equal to the imaginary part of the antenna 203 impedance ZA. The resistance ‘left out’ after the antenna reactance cancelation is transformed to a system impedance (usually 50 ohms) using the additional passive resistance matching network 205.
There are two important problems that limit the widespread use of a non-Foster matching for transmitting applications, based on the principle explained in FIG. 2: the design of an efficient NIC, and the assurance of a stable operation without unwanted oscillations. Due to aforementioned problems, there are only a few publicly available documents that report on non-Foster-matched transmitters and they only demonstrate limited success.
Improved efficiency with non-Foster matching of the transmitting antenna has been reported experimentally in Stephen E. Sussman-Fort, Ron M. Rudish, “Non Foster Impedance Matching for Transmit Applications,” 2006 IEEE International Workshop on Antenna Technology Small Antennas and Novel Metamaterials, pp. 53-56, Mar. 6-8, 2006; S. E. Sussman-Fort, R. M. Rudish, “Increasing Efficiency or Bandwidth of Electrically-Small Transmit Antennas by Impedance Matching With Non-Foster Circuits,” PIERS 2006, Mar. 26-29, 2006. A different approach that, instead of direct antenna matching, uses a non-Foster network embedded within a transmitting power amplifier, was proposed theoretically in M. W. Yung and D. A Hitko, “Non-Foster Impedance Power Amplifier”, U.S. Pat. No. 8,374,561 B1.
Reaching stability in non-Foster networks (assurance of stable operation of a non-Foster circuit without unwanted self-oscillations) is a difficult problem. The difficulty comes from the fact that all existing designs of negative elements (i.e. all the realizations of NIC circuits that behave as negative capacitors or negative inductors) are based on amplifiers with positive feedback. Thus, all non-Foster circuits are inherently prone to instabilities. There have been several approaches to avoid occurrence of the instability. They are reported in E.Ugarte-Muñoz, S. Hrabar, D, Segovia-Vargas, A. Kiricenko, “Stability of Non-Foster Reactive Elements for use in Active Metamaterials and Antennas”, IEEE Tran. on AP-S, Vol. 60, No. 7, pp. 3490-3494, 2012; S. D. Stearns, “Non-Foster Circuits and Stability Theory,” IEEE International Symposium on Antennas and Propagation paper 326.1, pp. 1942-1945, Spokane, Wash., Jul. 3-8, 2011.; J. Loncar, S. Hrabar, D. Muha, “Stability of simple lumped-distributed networks with negative capacitors”, IEEE Transactions on Antennas and Propagation, vol. 65, no. 1, pp. 390-395, January 2017; Q. Tang, H. Xin, “Stability Analysis of Non-Foster Circuit Using Normalized Determinant Function”, IEEE Transactions on Microwave Theory and Techniques, Vol. 65, No. 9, Sep. 2017, pp. 3269-3277). In spite of all the efforts, a stability issue is still not well understood, which makes a design of stable non-Foster circuit extremely challenging engineering task. In practice, achieving a stable operation of an active non-Foster matching network usually requires many simulation-design-testing cycles, which is very tedious and expensive approach.
Apart from matching applications, the non-Foster elements are sometimes used for construction of the oscillators (Arthur J. Radclitfe, Jr., La Grange, III, “Negative-impedance Transistor Oscillator”, U.S. Pat. No. 2,852,680; Jieh-Tsong Wu, Wei-Zen Shen, Tou-Liu, “Variable Frequency LC Oscillator Using Variable Impedance and Negative Impedance Circuits, U.S. Pat. No. 5,486,794).
A conference report by S. Hrabar and A. Kiricenko, entitled “Towards Broadband Tunable non-Foster Radiating Systems”, 10th International Congress on Advanced Electromagnetic Materials in Microwaves and Optics (METAMATERIALS), pp. 133-135, 2016 proposed unusual approach of managing stability issue of active non-Foster matching in transmitting applications. Abovementioned report describes a self-oscillating non-Foster matching network connected to a short dipole antenna (a dipole antenna shorter than λ/10, λ being a wavelength of the signal).
A self-oscillating non-Foster matching network 300, is illustrated in FIG. 3A (PRIOR ART), shown to comprise a NIC 301 connected between the short dipole antenna 302 and a NIC load 303. The equivalent circuit 305 of the antenna 302 is shown in FIG. 3B (PRIOR ART), comprising a series combination of a resistor (RA) and a capacitor (CA). This series RC combination is the simplest equivalent circuit of a short dipole antenna. The NIC load 303, comprises substantially the same series combination of RA and CA as the antenna load, but the negative impedance converter (NIC) 301 transforms or inverts this positive impedance into a series circuit 304 with both negative capacitance and negative resistance as illustrated in FIG. 3B. The impedance of the NIC load seen through the NIC 301 appears as a series circuit 304 with resistance equal to −RA and capacitance equal to −CA. The mesh impedance, defined as a sum of all impedances across a closed loop, equal to zero, namely, −RA−jXA+RA+jXA=0, where XA is the capacitive reactance of the antenna 302. The definition of mesh impedance and system stability of such a system is described in publicly available documents, such as, S. D. Stearns, “Counterintuitive Aspects of Non-Foster Networks,” presentation Adelphi Antenna Workshop on Electrically Small Antennas, Clarksville, Md., July 8-9, 201. Because of the zero mesh impedance, the circuit system shown in FIG. 3B is a self-oscillating system that supports arbitrary signal waveform. In addition, all the energy generated by the negative resistance (−RA) will be delivered to the antenna 302. In other words, all of the energy generated will be radiated by the antenna 302. Thus, the system represented by a circuit in FIG. 3B is perfectly matched.
The same system with the addition of a series resonant circuit 306 disposed between the antenna impedance 307 and the inverted NIC load impedance 308 is represented by a circuit in FIG. 3C. This consists of the negative RC circuit 308, connected to the antenna 307, via an additional series LC circuit 306. The purpose of the circuit 306 is tuning of a sinusoidal oscillating signal to any desired frequency. FIG. 3C actually depicts a tunable, perfectly matched, antenna-transmitter system. The antenna-transmitter system shown has theoretically an infinite tuning bandwidth with perfect matching. For this circuit, the inherent instability of the non-Foster circuit (the NIC 301, the antenna 302 and the load 303) is a desirable property of the system. Experimental verification of aforementioned idea (depicted in FIG. 3) was presented in the conference report by S. Hrabar, A. Kiricenko, and I. Krois, entitled “Antenna-transmitter based on Non-Foster Source”, Proceedings of the 2017 IEEE International Symposium on Antennas and Propagation (APS/URSI), July 2017.
Although abovementioned antenna-transmitter system (depicted in FIGS. 3A, 3B, and 3C) has demonstrated a marked improvement in non-Foster transmission, several issues remain: firstly, an equivalent circuit of a short dipole antenna that comprises only one resistor and only one capacitor is not an excellent approximation, only valid within the narrow bandwidth. Due to the change of antenna impedance with frequency, both the antenna-transmitter tuning bandwidth and the impedance matching will always be significantly narrower than predicted using a simple RC model of a short antenna. Secondly, due to inevitable antenna imperfections as well as the influence of nearby objects on antenna properties, the impedance of the antenna in a realistic transmitting scenario cannot be predicted accurately. Thus, it would be necessary to measure the impedance of used short dipole antenna beforehand and, using measured data, to design a dedicated RC network used as the NIC load (the load 303 in FIG. 3A (PRIOR ART). This is impractical as each antenna requires a specially designed NIC load and does not allow a simple use of different antennas in different applications.
It is clear that a need in the industry still remains for a tunable RF antenna-transmitter system that exhibits operation over a wide band. This disclosure addresses the design that overcomes aforementioned drawbacks and assures broadly tunable self-oscillations with perfect matching, without a specially designed NIC load.